Q1. In which of the following expressions ‘W > Z’ as well as ‘ Y > Z’ hold definitely true?
A. W > X > U = Z < H ≤ Y
B. W ≥ X = U > Z ≤ H < Y
C. W = X > U ≥ Z < H < Y
D. All of the above
E. None of the above
EXPLANATION
In order to ensure the statement that holds ‘ W > Z’ and ‘ Y > Z’ definitely true, we have to check all the options one by one.
For option A :
W > X > U = Z < H ≤ Y
Here, the common sign between W and Z is ‘>’, thus it follows W > Z.
The common sign between Z and Y is also ‘<‘ , thus it follows Z < Y or Y > Z.
For option B :
W ≥ X = U > Z ≤ H < Y
Here also, the common sign between W and Z is ‘>’, thus it follows W > Z.
The common sign between Z and Y is also ‘<‘ , thus it follows Z < Y or Y > Z.
For option C :
W = X > U ≥ Z < H < Y
Here again, the common sign between W and Z is ‘>’, thus it follows W > Z.
The common sign between Z and Y is also ‘<‘ , thus it follows Z < Y or Y > Z.
Since all the three expressions hold the given conclusions true, option D “all of the above” is correct.
Hence option D is correct.
Q2. Which of the following symbols must replace the question mark in the following equation so that R < L is definitely true and F > P is not definitely false?
M ≥ F > R = Q ? K ≤ L = P
A. >
B. =
C. ≤
D. <
E. Either option A or B
EXPLANATION
Let us check each of the options one by one.
Option A :
M ≥ F > R = Q > K ≤ L = P
In this case, we can see the opposite signs between R and L, so we can’t say that R > L is definitely true.Thus option A is incorrect.
Option B :
M ≥ F > R = Q = K ≤ L = P
In this case R ≤ L, this means that either R < L or R = L . thus R < L is not definitely true. Thus option B is incorrect.
Option C :
M ≥ F > R = Q ≤ K ≤ L = P
In this case also R ≤ L, this means that either R < L or R = L . thus R < L is not definitely true. Thus option C is incorrect.
Option D :
M ≥ F > R = Q < K ≤ L = P
Here we can see that R < L is definitely true.
There are opposite signs between F and P, so following 3 ewlationships is posible between F and P – F > P, F = P or F < P. Thus we can say that F > P is not definitely false.
Hence option D is correct.
Q3. Which of the following symbols must replace the question mark in the following equation so that A < S is definitely true and B > L is not definitely true?
D < A ≤ L = C ? T ≤ B < S
A. =
B. <
C. ≤
D. Either option A or C
E. Either option A or B
EXPLANATION
Let us check each of the options one by one.
Option A :
D < A ≤ L = C = T ≤ B < S
In this case A < S is definitely true and B > L is not definitely true. Thus option A is correct.
Option B :
D < A ≤ L = C < T ≤ B < S
In this case A < S is definitely true but B > L is also definitely true. Thus option B is incorrect.
Option C :
D < A ≤ L = C ≤ T ≤ B < S
In this case A < S is definitely true as well as we can see that B > L is not definitely true, B = L could also be a possible true statement.
Thus option C is also correct.
Therefore with the help of either option A or option C can derive the desired conclusions.Hence option D is correct.